Papers › Optimizing positive maps in the matrix algebra Mₙ
Optimizing positive maps in the matrix algebra Mₙ
Anindita Bera, Gniewomir Sarbicki, Dariusz Chruściński
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We present an optimization procedure for a seminal class of positive maps τ_(n,k) in the algebra of n ×n complex matrices introduced and studied by Tanahasi and Tomiyama, Ando, Nakamura and Osaka. Recently, these maps were proved to be optimal whenever the greatest common divisor GCD(n,k)=1. We attain a general conjecture how to optimize a map τ_(n,k) when GCD(n,k)=2 or 3. For GCD(n,k)=2, a series of analytical results are derived and for GCD(n,k)=3, we provide a suitable numerical analysis.
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